For simplicity, throughout this paper we consider the two-dimensional square domain \(\Omega =(0,L)\times (0,L)\) 
for the equation (REF ) equipped with periodic boundary conditions. Note that the extensions to three-dimension problems and
homogeneous Neumann boundary condition are straightforward. For other feasible spatial discretization, we refer to [1]} for more details.
In this section, we first present some notations related to the spatial discretization by central finite difference, then
briefly review the classic SAV schemes for time integration.
